Pari/GP, 42 bytes

Using the built-in qfrep.

n->1+2*vecsum(Vec(qfrep([2,1;1,2],n^2,1)))

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Pari/GP, 42 bytes

Using the built-in qfrep.

n->1+2*vecsum(Vec(qfrep([2,1;1,2],n^2,1)))

qfrep(q,B,{flag=0}): vector of (half) the number of vectors of norms from 1 to B for the integral and definite quadratic form q. If flag is 1, count vectors of even norm from 1 to 2B.

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Pari/GP, 46 bytes

Based on OEIS A004016.

n->1+6*sum(i=1,n^2,sumdiv(i,d,kronecker(d,3)))

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Pari/GP, 42 bytes

Using the built-in qfrep.

n->1+2*vecsum(Vec(qfrep([2,1;1,2],n^2,1)))

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